document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=694702>Question 694702</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This one is kinda urgent..please i will appreciate ANY kind of help-<BR>\n" );
document.write( "\"Imagine that you are on a street<BR>\n" );
document.write( "with houses marked 1 through n. There is a<BR>\n" );
document.write( "house in between (x) such that the sum of<BR>\n" );
document.write( "the house numbers to left of it equals the<BR>\n" );
document.write( "sum of the house numbers to its right. If n is<BR>\n" );
document.write( "between 50 and 500, what are n and x?\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #428483 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=428483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I do not see the whole elegant solution, but maybe this helps.<BR>\n" );
document.write( "A sum of consecutive house numbers is the sum of an arithmetic sequence/progression, which can be calculated as the average of the first and last terms, times the number of terms.<BR>\n" );
document.write( "The sum of the numbers of the houses to one side is<BR>\n" );
document.write( "1+2+3+ ... +(x-2)+(x-1)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B%28x-1%29%29%28x-1%29%2F2=x%28x-1%29%2F2 ALIGN=MIDDLE  ALT=\"%281%2B%28x-1%29%29%28x-1%29%2F2=x%28x-1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sum of the numbers of the houses to the other side is<BR>\n" );
document.write( "(x+1)+(x+2)+ ... +(n-1)+n=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%2Bn%29%28n-x%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%2B1%2Bn%29%28n-x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-1%29%2F2=%28x%2B1%2Bn%29%28n-x%29%2F2 ALIGN=MIDDLE  ALT=\"x%28x-1%29%2F2=%28x%2B1%2Bn%29%28n-x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-1%29=%28x%2B1%2Bn%29%28n-x%29 ALIGN=MIDDLE  ALT=\"x%28x-1%29=%28x%2B1%2Bn%29%28n-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x=n%5E2%2Bn-n%5E2-x ALIGN=MIDDLE  ALT=\"x%5E2-x=n%5E2%2Bn-n%5E2-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2=n%5E2%2Bn ALIGN=MIDDLE  ALT=\"2x%5E2=n%5E2%2Bn\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2=n%28n%2B1%29 ALIGN=MIDDLE  ALT=\"2x%5E2=n%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since they are consecutive integers,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1 ALIGN=MIDDLE  ALT=\"n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot have any common factors.<BR>\n" );
document.write( "For their product to be twice a perfect square, we need two perfect squares with no common factors:<BR>\n" );
document.write( "one perfect square will be a factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and another perfect square will be a factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1 ALIGN=MIDDLE  ALT=\"n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Calling the larger one <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28n=a%5E2%2C%28n%2B1%29%2F2=b%5E2%29 ALIGN=MIDDLE  ALT=\"system%28n=a%5E2%2C%28n%2B1%29%2F2=b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2=a%5E2%2B1 ALIGN=MIDDLE  ALT=\"2b%5E2=a%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=2b%5E2-1 ALIGN=MIDDLE  ALT=\"a%5E2=2b%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28n%2F2=b%5E2%2Cn%2B1=a%5E2%29 ALIGN=MIDDLE  ALT=\"system%28n%2F2=b%5E2%2Cn%2B1=a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%2B1=a%5E2 ALIGN=MIDDLE  ALT=\"2b%5E2%2B1=a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "for some mutually prime positive integers <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3Eb ALIGN=MIDDLE  ALT=\"a%3Eb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "whose squares must be between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=50%2F2 ALIGN=MIDDLE  ALT=\"25=50%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=501 ALIGN=MIDDLE  ALT=\"501\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%29=5 ALIGN=MIDDLE  ALT=\"sqrt%2825%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28501%29%3C23 ALIGN=MIDDLE  ALT=\"sqrt%28501%29%3C23\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we should look at numbers from 5 to 22.<BR>\n" );
document.write( "As the larger square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an odd number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=2b%5E2+%2B-+1 ALIGN=MIDDLE  ALT=\"a%5E2=2b%5E2+%2B-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an odd number, and cannot be 22, so we should look at numbers from 5 to 22.<BR>\n" );
document.write( "We are looking for a pair such that the square of the larger number is one more or one less than double the square of the smaller number.<BR>\n" );
document.write( "We try numbers from 5 on as the smaller number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and see what works.<BR>\n" );
document.write( "I tried them making a table, which is hard for me to render here, so I will just show the calculations.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=5 ALIGN=MIDDLE  ALT=\"b=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2=2%2A5%5E2=50 ALIGN=MIDDLE  ALT=\"2b%5E2=2%2A5%5E2=50\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2-1=49%3C50 ALIGN=MIDDLE  ALT=\"2b%5E2-1=49%3C50\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%2B1=51 ALIGN=MIDDLE  ALT=\"2b%5E2%2B1=51\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2=2%2A6%5E2=72 ALIGN=MIDDLE  ALT=\"2b%5E2=2%2A6%5E2=72\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2-1=71 ALIGN=MIDDLE  ALT=\"2b%5E2-1=71\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%2B1=73 ALIGN=MIDDLE  ALT=\"2b%5E2%2B1=73\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=7 ALIGN=MIDDLE  ALT=\"b=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2=2%2A7%5E2=98 ALIGN=MIDDLE  ALT=\"2b%5E2=2%2A7%5E2=98\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2-1=97 ALIGN=MIDDLE  ALT=\"2b%5E2-1=97\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%2B1=99 ALIGN=MIDDLE  ALT=\"2b%5E2%2B1=99\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=8 ALIGN=MIDDLE  ALT=\"b=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2=2%2A8%5E2=128 ALIGN=MIDDLE  ALT=\"2b%5E2=2%2A8%5E2=128\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2-1=127 ALIGN=MIDDLE  ALT=\"2b%5E2-1=127\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%2B1=129 ALIGN=MIDDLE  ALT=\"2b%5E2%2B1=129\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=9 ALIGN=MIDDLE  ALT=\"b=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2=2%2A9%5E2=162 ALIGN=MIDDLE  ALT=\"2b%5E2=2%2A9%5E2=162\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2-1=161 ALIGN=MIDDLE  ALT=\"2b%5E2-1=161\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%2B1=163 ALIGN=MIDDLE  ALT=\"2b%5E2%2B1=163\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=10 ALIGN=MIDDLE  ALT=\"b=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2=2%2A10%5E2=200 ALIGN=MIDDLE  ALT=\"2b%5E2=2%2A10%5E2=200\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2-1=199 ALIGN=MIDDLE  ALT=\"2b%5E2-1=199\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%2B1=201 ALIGN=MIDDLE  ALT=\"2b%5E2%2B1=201\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=11 ALIGN=MIDDLE  ALT=\"b=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2=2%2A11%5E2=242 ALIGN=MIDDLE  ALT=\"2b%5E2=2%2A11%5E2=242\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2-1=241 ALIGN=MIDDLE  ALT=\"2b%5E2-1=241\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%2B1=243 ALIGN=MIDDLE  ALT=\"2b%5E2%2B1=243\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=12 ALIGN=MIDDLE  ALT=\"b=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2=2%2A6%5E2=288 ALIGN=MIDDLE  ALT=\"2b%5E2=2%2A6%5E2=288\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2-1=287 ALIGN=MIDDLE  ALT=\"2b%5E2-1=287\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%2B1=highlight%28289=17%5E2%29 ALIGN=MIDDLE  ALT=\"2b%5E2%2B1=highlight%28289=17%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The pair <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=12 ALIGN=MIDDLE  ALT=\"b=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=17 ALIGN=MIDDLE  ALT=\"a=17\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=2b%5E2%2B1 ALIGN=MIDDLE  ALT=\"a%5E2=2b%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , works with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28n%2F2=b%5E2%2Cn%2B1=a%5E2%29 ALIGN=MIDDLE  ALT=\"system%28n%2F2=b%5E2%2Cn%2B1=a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1=a%5E2 ALIGN=MIDDLE  ALT=\"n%2B1=a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1=17%5E2 ALIGN=MIDDLE  ALT=\"n%2B1=17%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1=289 ALIGN=MIDDLE  ALT=\"n%2B1=289\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n=288%29 ALIGN=MIDDLE  ALT=\"highlight%28n=288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2=n%28n%2B1%29 ALIGN=MIDDLE  ALT=\"2x%5E2=n%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2=288%2A289 ALIGN=MIDDLE  ALT=\"2x%5E2=288%2A289\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=288%2A289%2F2 ALIGN=MIDDLE  ALT=\"x%5E2=288%2A289%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=%0D%0A41616 ALIGN=MIDDLE  ALT=\"x%5E2=%0D%0A41616\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=204%29 ALIGN=MIDDLE  ALT=\"highlight%28x=204%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Since we expect only one solution, we could stop here.<BR>\n" );
document.write( "Otherwise we would try further to see that nothing else works.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=13 ALIGN=MIDDLE  ALT=\"b=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2=2%2A13%5E2=339 ALIGN=MIDDLE  ALT=\"2b%5E2=2%2A13%5E2=339\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2-1=337 ALIGN=MIDDLE  ALT=\"2b%5E2-1=337\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%2B1=339 ALIGN=MIDDLE  ALT=\"2b%5E2%2B1=339\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=14 ALIGN=MIDDLE  ALT=\"b=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2=2%2A14%5E2=392 ALIGN=MIDDLE  ALT=\"2b%5E2=2%2A14%5E2=392\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2-1=391 ALIGN=MIDDLE  ALT=\"2b%5E2-1=391\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%2B1=393 ALIGN=MIDDLE  ALT=\"2b%5E2%2B1=393\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=15 ALIGN=MIDDLE  ALT=\"b=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2=2%2A15%5E2=450 ALIGN=MIDDLE  ALT=\"2b%5E2=2%2A15%5E2=450\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2-1=449 ALIGN=MIDDLE  ALT=\"2b%5E2-1=449\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%2B1=451 ALIGN=MIDDLE  ALT=\"2b%5E2%2B1=451\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%3E=16 ALIGN=MIDDLE  ALT=\"b%3E=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%3E=2%2A16%5E2=512 ALIGN=MIDDLE  ALT=\"2b%5E2%3E=2%2A16%5E2=512\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%5E2%2B1%3E2b%5E2-1%3E=511%3E501 ALIGN=MIDDLE  ALT=\"2b%5E2%2B1%3E2b%5E2-1%3E=511%3E501\"   DISABLED_style= \"max-width:90%; height:auto;\" >=not a number that could be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1 ALIGN=MIDDLE  ALT=\"n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );